In the March/April issue of <em>CiSE</em>, we discussed the geometry of linear and algebraic systems. We also defined ideals and bases so that we could introduce the concept of Gr?bner bases for algebraic system solving. In this article, we give more details about Gr?bner bases and describe their main application (algebraic system solving) along with some surprising derived ones: inclusion of varieties, automatic theorem-proving in geometry, expert systems, and railway interlocking systems.